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Chapter 1: 21 (page 28)

In Wagner鈥檚 opera Das Rheingold,the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of gold is 19.3 g/cm3, and take its value to be about $10 per gram.

Short Answer

Expert verified

The monetary value of the pile is $69.68 million dollar.

Step by step solution

01

Mass of pile

The dimension of the pile is 18in脳18in脳68in.

The volume of pile in cm3 will be,

V=18in脳18in脳68inV=22032in3脳2.54cm1in3V=361039.794cm3

Since the density of gold is role="math" localid="1647983648972" 蚁=19.3g/cm3.

The mass of gold can be calculated as,

m=蚁Vm=19.3g/cm3361039.794cm3m=6968068.025g

02

The calculation for monetary value

The price per gram is c=$10/g.

The price of the pile can be calculated as,

role="math" localid="1647984248778" C=mcC=6968068.025g$10/gC=6968068.025g脳1million106C=69.68milliondollar

Thus, the monetary value of the pile is $69.68 million dollar.

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